Question

Find f(x) and g(x) so the function can be expressed as y = f(g(x)).
y = 8/x^2 + 4

Answer 1

There can be several such functions. I am giving you one example here and then try finding out one yourself:

Let f(x) = 8x + 4

and g(x) = \(\cfrac{1}{x^2}\)

Then,

f(g(x)) = 8\(\cfrac{1}{x^2}\) + 4 = y

Answer 2

I don't understand

Answer 3

Okay let me help you.

Answer 4

First of all you have two options you can either assume f(x) or g(x).

Answer 5

For example, in the example I wrote above , I assumed f(x) first,

f(x) = 8x + 4

What I actually did was I observed y carefully. See if I forget the 1/x^2 part in y and replace it with "?" I get;

y = 8? + 4

Right ?

Answer 6

@Andshedances1234 ??

Answer 7

I'm here, im trying to think lol. Why would you forget the x^2?

Answer 8

So that I can easily assume f(x) and g(x)

Answer 9

I am just replacing 1/x^2 by some other symbol "?"

Answer 10

Okay, so we assumed f(x)? What about g(x)

Answer 11

You can easily obtain g(x) once you have assumed f(x).

See:

I have y = 8? + 4

Ok?

Answer 12

right

Answer 13

Good now for my example, I assumed f(x) = "?"

Okay ?

Answer 14

ok

Answer 15

Now,

what we actually do by doing f(g(x)) is in place of x in f(x) we put g(x). Do you get this ?

for example, take a very different example,

suppose f(x) = 2x

Now, if I replace x by g(x), then f(x) will change to f(g(x))

So, f(g(x)) = 2g(x)

Answer 16

Do you get this part ?